We explored this inductive bias by instantiating Recurrent GNN encoders, which can be trained for a certain amount of message passing steps/layers (\(L\) -train), but can perform more rounds of message passing (\(L\) -eval) during inference [1]}, [2]}.
To do so, we leverage the Encode-Process-Decode architectural paradigm [3]}, which has shown promising generalization for physics simulation engines [4]}, graph algorithms [5]}, [6]} and SAT problems [7]}.
We redefine the GNN encoder from Section REF  to use a shared Gated Recurrent Unit-based block across message passing steps:
\(h_i^{\ell +1} &=& \text{GRU} \Big ( \textsc {Aggr}_{j \in \mathcal {N}_i} \Big ( \sigma (e_{ij}^{\ell }) \odot V h_j^{\ell } \Big ) \ , \ h_i^{\ell } \Big ) \ ,  \\e_{ij}^{\ell +1} &=& \text{GRU} \Big ( B h^{\ell }_i + C h^{\ell }_j \ , \ e_{ij}^{\ell } \Big ) \ , \) 
